Related papers: Galactic Dark Matter and Bertrand Space-times
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
Many cosmological observations call for the existence of dark matter. The most direct evidence for dark matter is inferred from the measured flatness of galactic rotation curves. The latter is based on Newtonian gravity. Alternative…
Einstein originally proposed a nonsymmetric tensor field, with its symmetric part associated with the spacetime metric and its antisymmetric part associated with the electromagnetic field, as an approach to a unified field theory. Here we…
Certain solutions to a gravitational form of Schrodinger's equation can yield stable, macroscopic eigenstate solutions having no classical analogue, with properties resembling those of dark matter. Some more tractable solutions show: (1)…
The study of the rotation curves of spiral galaxies reveals a nearly constant cored density distribution of Cold Dark Matter. N-body simulations however lead to a cuspy distribution on the galactic scale, with a central peak. A…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…
Analyzing the static spherically symmetric and rotating ellipsoid solutions in the Newtonian limit of Jordan, Brance - Dicke theory we find the following. In empty space scalar-tensor theories have trivial solution of field equation with…
An exact solution of Einstein's field equations for a static spherically symmetric medium with a radially boost invariant energy-momentum tensor is presented. In the limit of an equation of state corresponding to a distribution of radially…
It is shown that an arbitrary static, spherically symmetric metric can be presented as an exact solution of a scalar-tensor theory (STT) of gravity with certain nonminimal coupling function $f(\phi)$ and potential $U(\phi)$. The scalar…
We find a new family of galactic metrics corresponding to flat rotation curves at the outer radii. These are vacuum solutions to a gravity theory where the Newton's coupling varies mildly in space. The effective `mass', whose origin is…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
The observed rotation curves of low surface brightness (LSB) galaxies play an essential role in studying dark matter, and indicate that there exists a central constant density dark matter core. However, the cosmological N-body simulations…
We establish an algorithm that produces a new solution to the Einstein field equations, with an anisotropic matter distribution, from a given seed isotropic solution. The new solution is expressed in terms of integrals of known functions,…
Dark matter consisting of a Bose--Einstein condensate (BEC) of ultra-light particles is predicted to have a soliton shape that shifts with the dark matter mass fraction in galaxies containing a centrally localized point mass (or black…
This paper explores ``black hole'' solutions of various Einstein-wave matter systems admitting an isometry of their domain of outer communications taking every point to its future. In the first two parts, it is shown that such solutions,…
The observed strong dark-to-luminous matter coupling suggests the existence of a some functional relation between visible and DM sources which leads to biased Einstein equations. We show that such a bias appears in the case when the…
We study gravitational collapse with anisotropic pressures, whose end stage can mimic space-times that are seeded by galactic dark matter. To this end, we identify a class of space-times (with conical defects) that can arise out of such a…
We investigate the static and spherically symmetric solutions of Einstein's equations for a scalar field with non-canonical kinetic term, assumed to provide both the dark matter and dark energy components of the Universe. In particular, we…
We study the linear stability of vacuum static, spherically symmetric solutions to the gravitational field equations of the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories (STT) of gravity, restricting ourselves to nonphantom…